Optimal Sales Schemes against Interdependent Buyers

Under the optimal scheme identified in Theorem 2, the response by each buyer moves in the direction of the response dominant among their predecessors. In other words, a buyer accepts with a higher probability than his predecessor when most buyers before him have chosen to accept, and rejects with a higher probability when most buyers before him have chosen to reject. Formally, the following proposition states that when the state αt−1 > 0 as a result of many buyers having accepted, the expected probability that the next buyer accepts is higher than the probability that the current buyer accepts. Conversely, when the state αt−1 < 0 as a result of many buyers having rejected, the expected probability that the next buyer rejects is higher than the probability that the current buyer rejects.